试求 $$ex vlm{n}n^2sex{x^frac{1}{n}-x^frac{1}{n+1}},quad x>0. eex$$
解答: $$eex ea mbox{原极限} &=vlm{n}n^2cdot x^xiln xsex{frac{1}{n}-frac{1}{n+1}}quadsex{frac{1}{n+1}<xi<frac{1}{n}}\ &=ln x. eea eeex$$
试求 $$ex vlm{n}n^2sex{x^frac{1}{n}-x^frac{1}{n+1}},quad x>0. eex$$
解答: $$eex ea mbox{原极限} &=vlm{n}n^2cdot x^xiln xsex{frac{1}{n}-frac{1}{n+1}}quadsex{frac{1}{n+1}<xi<frac{1}{n}}\ &=ln x. eea eeex$$